1,303 research outputs found
Spectral learning of general weighted automata via constrained matrix completion
Student Paper Awards NIPS 2012Many tasks in text and speech processing and computational biology require estimating
functions mapping strings to real numbers. A broad class of such functions
can be defined by weighted automata. Spectral methods based on the singular
value decomposition of a Hankel matrix have been recently proposed for
learning a probability distribution represented by a weighted automaton from a
training sample drawn according to this same target distribution. In this paper, we
show how spectral methods can be extended to the problem of learning a general
weighted automaton from a sample generated by an arbitrary distribution. The
main obstruction to this approach is that, in general, some entries of the Hankel
matrix may be missing. We present a solution to this problem based on solving a
constrained matrix completion problem. Combining these two ingredients, matrix
completion and spectral method, a whole new family of algorithms for learning
general weighted automata is obtained. We present generalization bounds for a
particular algorithm in this family. The proofs rely on a joint stability analysis of
matrix completion and spectral learning.Peer ReviewedAward-winningPostprint (published version
Complexity of Equivalence and Learning for Multiplicity Tree Automata
We consider the complexity of equivalence and learning for multiplicity tree
automata, i.e., weighted tree automata over a field. We first show that the
equivalence problem is logspace equivalent to polynomial identity testing, the
complexity of which is a longstanding open problem. Secondly, we derive lower
bounds on the number of queries needed to learn multiplicity tree automata in
Angluin's exact learning model, over both arbitrary and fixed fields.
Habrard and Oncina (2006) give an exact learning algorithm for multiplicity
tree automata, in which the number of queries is proportional to the size of
the target automaton and the size of a largest counterexample, represented as a
tree, that is returned by the Teacher. However, the smallest
tree-counterexample may be exponential in the size of the target automaton.
Thus the above algorithm does not run in time polynomial in the size of the
target automaton, and has query complexity exponential in the lower bound.
Assuming a Teacher that returns minimal DAG representations of
counterexamples, we give a new exact learning algorithm whose query complexity
is quadratic in the target automaton size, almost matching the lower bound, and
improving the best previously-known algorithm by an exponential factor
Spectral regularization for max-margin sequence tagging
We frame max-margin learning of latent variable structured prediction models as a convex optimization problem, making use of scoring functions computed by input-output observable operator models. This learning problem can be expressed as an optimization problem involving a low-rank Hankel matrix that represents the inputoutput operator model. The direct outcome of our work is a new spectral regularization method for max-margin structured prediction. Our experiments confirm that our proposed regularization framework leads to an effective way of controlling the capacity of structured prediction models.Peer ReviewedPostprint (published version
Some improvements of the spectral learning approach for probabilistic grammatical inference
International audienceSpectral methods propose new and elegant solutions in probabilistic grammatical inference. We propose two ways to improve them. We show how a linear representation, or equivalently a weighted automata, output by the spectral learning algorithm can be taken as an initial point for the Baum Welch algorithm, in order to increase the likelihood of the observation data. Secondly, we show how the inference problem can naturally be expressed in the framework of Structured Low-Rank Approximation. Both ideas are tested on a benchmark extracted from the PAutomaC challenge
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